This invention relates to spectroscopy wherein specific frequency signals related to physical events of interest occur simultaneously with other frequency signals and, in particular, to the use of a Discrete Fourier Transform in spectroscopy or other similar analyzing techniques wherein a plurality of simultaneously occurring physical events manifest themselves in the form of periodic oscillations.
As one example of the spectroscopies exhibiting these features, there is disclosed in U.S. Pat. No. 3,937,955 to Comisarow et al, a multi-channel ion cyclotron resonance (ICR) mass spectrometer that utilizes Fast Fourier Transform (FFT) to analyze an entire range of frequencies. A gas sample is introduced into the ICR cell where molecular species contained in a sample are ionized and then excited whereby the ions orbit at different frequencies determined by their mass. The image current produced by the orbiting ions is sensed and a waveform generated that contains information relating to the species present in the sample. The waveform data is digitized and the digitized information transformed using a Fast Fourier Transform (FFT) operation.
The use of FFT in an ICR instrument offers rapid means for analyzing various types of samples and is an effective method by which the entire spectrum within the range of the instrument can be examined. The characteristics of FFT are, however, not truly compatible with the ICR sensor because the sensor frequencies are inversely related to the mass of ions present in a sample, while the FFT analysis occurs at fixed frequency intervals and requires that all frequencies within the spectrum be analyzed. As a practical result, much of the available instrument computer power is expended on analyzing segments of the spectrum that contains either no information at all or information that is of no analytical interest to the user because the frequency or frequencies of interest occur only in a small segment of the overall spectrum.
It should be further noted that the resolution of a FFT instrument is also limited by the amount of time and computer power available to resolve all frequencies within the instrument's spectral range without regard to what the spectrum contains or, more importantly, does not contain. This again places a heavy demand on the instrument in terms of time and power and, as a consequence, the cost of building and operating a high resolution instrument is typically high.